Roulette. An American roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers. Suppose that you bet $10 on red. If the ball lands on a red number, you win$10; otherwise, you lose your $10.

Letx be the amount you win on your $10 bet.

(a) Write down the probability distribution ofx. [4pts]

(b) Calculate the mean ofx.Give an interpretation of the mean. [4pts]

Solution.

X denotes the amount of money you could win in one game.

(a)

X	P(X=x)
10	18/38
-10	20/38

c) The mean of X is 10*18/38+(-10)*20/38=-0.526 which means that on average you could lose $0.526.